Matrix-Valued Levelings for Colour Images

  • Michael BreußEmail author
  • Laurent Hoeltgen
  • Andreas Kleefeld
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10225)


Morphological levelings represent a useful tool for the decomposition of an image into cartoon and texture components. Moreover, they can be used to construct a morphological scale space. However, the classic construction of levelings is limited to the use of grey scale images, since an ordering of pixel values is required.

In this paper we propose an extension of morphological levelings to colour images. To this end, we consider the formulation of colour images as matrix fields and explore techniques based on the Loewner order for formulating morphological levelings in this setting. Using the matrix-valued colours we study realisations of levelings relying on both the completely discrete construction and the formulation using a partial differential equation. Experimental results confirm the potential of our matrix-based approaches for analysing texture in colour images and for extending the range of applications of levelings in a convenient way to colour image processing.


Mathematical morphology Dilation Erosion Loewner order Leveling 


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Michael Breuß
    • 1
    Email author
  • Laurent Hoeltgen
    • 1
  • Andreas Kleefeld
    • 2
  1. 1.Institute for MathematicsBrandenburg Technical UniversityCottbusGermany
  2. 2.Forschungszentrum Jülich, Institute for Advanced Simulation, Jülich Supercomputing CentreJülichGermany

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